SOME LACUNARY POWER SERIES AND MAHLER'S U-m-NUMBERS IN p-ADIC DOMAIN

Abstract

In this paper, we consider some lacunar power series in Q(p), where p is a prime number. We obtain some results about lacunary power series with rational coefficients for U-m-number arguments in Q(p). We determined whether the values of the considered lacunar power series belong to a certain field of algebraic numbers or to the set of transcendental numbers in Q(p). Also, we find similar results for lacunary power series with p-adic algebraic coefficients.